Patients 16 years of age and older who have kidney cancer that has spread beyond the kidney or whose primary kidney tumor has been removed within 6 months before entering the study and are at high risk for disease recurrence may be eligible for this study. Patients must have tissue type human leukocyte antigen serotype within HLA-A A serotype group (HLA-A2) or human leukocyte antigen serotype within HLA-A A serotype group (HLA-A3) (determined by a blood test for human leukocyte antigen (HLA) typing) and their tumors must produce the FGF-5 peptide. Candidates are screened with a physical examination, blood and urine tests, electrocardiogram (EKG), tumor biopsy (removal of a small sample of tumor for examination) in patients whose tumor is easily accessible, and scans (computed tomography (CT), bone scans) and x-rays if current scans are not available.